Curve Fitting to Planar Data

平面数据的曲线拟合

• 批准号: 09640281
• 负责人: SAKAI Manabu
• 金额: $ 1.6万
• 依托单位: KAGOSHIMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640281/
• 关键词: curve fitting; shape preserving; curvature; singularity; inflection points; Mathematica; spline; spiral; 平面データ; スパライラル; スパイラル; 計算の手間

In this project, first we have obtained the distribution of inflection points and singularities on a parametric rational cubic curve segment with aid of Mathematica(A System for Doing Mathematics by Computer). The reciprocal numbers of the magnitudes of the end slopes determine the occurrence of inflection points and singularities on the segment Its use enables us to check whether the segment has inflection points ora singularity (a loop or a cusp) and to get an idea how to place control vertices and how to choose weights for the rational Bezier cubic curve segment to preserve the fair shape. Spiral segments have several advantages of containing neither inflection points, singularities nor curvature extrema. Next, we have given (i) an easy to use condition for a planar T- cubic .segment to be a spiral in terms of the reciprocal numbers of the magnitudes of the end slopes, (ii) the explicit form of the T-cubic spiral, and (iii) simple algorithms for forming a T-cubic spiral and an arc/T-cubic spiral. We have also discussed which spirals should be used according to the angles of the tangent vectors at the data points. These results are useful for generating planar "visually pleasing", "shape preserving" approximations to a set of planar data points.

在本课题中，我们首先借助Mathematica（计算机数学处理系统）得到了参数有理三次曲线段上的拐点和奇点的分布。末端斜率的大小的倒数决定了段上拐点和奇点的出现。它的使用使我们能够检查段是否有拐点或奇点（环或尖点），并了解如何放置控制顶点以及如何为有理Bezier三次曲线段选择权重以保持公平的形状。螺旋段具有不包含拐点、奇点或曲率极值的几个优点。其次，我们给出了（i）平面T-三次线段是螺旋线的一个容易使用的条件，（ii）T-三次螺旋线的显式形式，（iii）形成T-三次螺旋线和弧/T-三次螺旋线的简单算法。我们还讨论了根据数据点处切向量的角度应该使用哪些螺旋线。这些结果是有用的生成平面的“视觉上令人愉快的”，“形状保持”近似的一组平面数据点。

项目成果

Masaharu Nakasima: "Stability of variable coefficients Runge-Kutta methods" 4th International Conference on Numerical methods and applications (Sofia Univ., Bulgaria, 19-23 August, 1998).

Masaharu Nakasima：“可变系数龙格-库塔方法的稳定性”第四届国际数值方法和应用会议（保加利亚索菲亚大学，1998 年 8 月 19-23 日）。

Masaharu Nakasima: "Stability of variable coefficient Runge-Kutta methds" 4th International Conference on Numerical methods and applications (Sofia Univ., Bulgaria, 19-23 August, 1998). (in press).

Masaharu Nakasima：“可变系数龙格-库塔方法的稳定性”第四届国际数值方法和应用会议（保加利亚索菲亚大学，1998 年 8 月 19-23 日）。

厚見〓司: "Short profoots of Hiramine' results on character values" Osaka J.Math.印刷中.

Tsukasa Atsumi：“Hiramine 的短篇小说对人物价值观的影响”Osaka J.Math 正在出版。

Manabu Sakai: "Rational segments with specified tangents and curvatures" Rep.Fac.Sci.Kagoshima Univ.31. 19-30 (1998)

Manabu Sakai：“具有指定切线和曲率的有理线段”Rep.Fac.Sci.Kagoshima Univ.31。

酒井,宦: "Planar Hermite spiral interpolation" Computer Aided Geomatric Design. 印刷中.

Sakai, Hiroshi：“平面 Hermite 螺旋插值”计算机辅助几何设计正在出版。